5 There are 5 times as many chickens as horses on a farm.

Solve the linear inequality: x ≤ -x + 4

Sophie [7]

Answer:

x ≤ 2

Step-by-step explanation:

i hope this helps :)

3 0

3 years ago

What is the value of x? A. 25° B. 50° C. 55° D. 75° E. 80°

Troyanec [42]

Answer:

<h2>Option B</h2><h2>x = 50° </h2>

Step-by-step explanation:

By the condition, 

25° + 105° + x = 180° [Angle sum property of triangle]

=> 130 + x = 180

=> x = 180 - 130

=> x = 50° (Ans)

6 0

3 years ago

Read 2 more answers

Find the volume of the rectangular prism. Express your answer as a simplified mixed number.

OverLord2011 [107]

Answer:

Volume = = 138⁶/32 cubic meters

Step-by-step explanation:

Given:

Length = 8⅜ m

Width = 2 m

Height = 8¼ m

Required:

Volume as a mixed number

Solution:

Volume of rectangular prism = L*W*H

Plug in the values

V = 8⅜ × 2 × 8¼

Change to improper fraction

V = 67/8 × 2 × 33/4

= (67 × 2 × 33)/(8 × 4)

= 4,422/32

= 138⁶/32 m³

7 0

3 years ago

In this triangle, which of the following is true?

Svetradugi [14.3K]

We know that this is a right triangle, so one of the sides has to be 90 (indicated by the square on the corner) The angles of all triangles must add to exactly 180. Subtract 90 and 35 from 180

If we do that, we get 55. We know that the unknown angle is 55 now. Now, it asks us for b. We can pythagoras theorem which states that (a^2 + b^2 = c^2) We already know c (c is 20) It does not tell us 2 of the sides but we do know that the answer is either B or D.

The side opposite of 90* should be the largest. The size opposite of 55 would be the second largest one. The side opposite of 35 would be the smallest one. Using pythagoras theorem again, I can try plugging in both 11.47 and 16.38 with c^2 - b^2 = a^2

11.47:

400 - 132 =268 (sq root now = 16.37) this would mean that A is larger than B. B should be larger than A. Try the other one

16.37:

400 -268 = 132 (sq root = 16.37) this would mean that B is larger than A which is what we want.

Thus, 16.37 = B and the last option would be correct (D)

Hope this helps, give an honest rating for me please

7 0

3 years ago

Give the expression 4n^2t/2n^t-1, write the expression as a binomial.

lubasha [3.4K]

binomial is an algebraic expression containing 2 terms. For example, (x + y) is a binomial.

We sometimes need to expand binomials as follows:

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

(a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

Clearly, doing this by direct multiplication gets quite tedious and can be rather difficult for larger powers or more complicated expressions.

Pascal's Triangle

We note that the coefficients (the numbers in front of each term) follow a pattern. [This was noticed long before Pascal, by the Chinese.]

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

You can use this pattern to form the coefficients, rather than multiply everything out as we did above.

The Binomial Theorem

We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.

Properties of the Binomial Expansion (a + b)nThere are \displaystyle{n}+{1}n+1 terms.The first term is an and the final term is bn.Progressing from the first term to the last, the exponent of a decreases by \displaystyle{1}1 from term to term while the exponent of b increases by \displaystyle{1}1. In addition, the sum of the exponents of a and b in each term is n.If the coefficient of each term is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we obtain the coefficient of the next term.

7 0

3 years ago